David, in November 2008 we did a BA SEA-LHR-CPT and return in first class. Originally there was no availability SEA-LHR and we were booked via YVR, but eventually, between 2-3 weeks before departure, the SEA-LHR leg opened up. If you haven't already, join their mileage program, that way you can search availability each day.

As to departure cities, in researching the trip on the BA board here on FT, the general consensus was that the F experience on the 744 was better than on the 777 as the cabin seemed more spacious. So you might want to see which of the cities you mentioned uses 744s and which 777s.

Have you checked PHX and DEN? I think BA flies out of there also.